{"id":5946,"date":"2013-06-01T22:46:09","date_gmt":"2013-06-01T14:46:09","guid":{"rendered":"http:\/\/morrisjfwong.com\/blog\/?p=5946"},"modified":"2014-07-23T10:05:38","modified_gmt":"2014-07-23T02:05:38","slug":"90-apples-puzzle-math-solution","status":"publish","type":"post","link":"https:\/\/morrisjfwong.com\/blog\/90-apples-puzzle-math-solution\/","title":{"rendered":"\u860b\u679c\u7684\u8b0e\u984c"},"content":{"rendered":"<p>\u860b\u679c\u7684\u8b0e\u984c: \u6211\u5011\u8981\u4f86\u89e3\u6c7a\u4e00\u500b90\u500b\u860b\u679c(90 apples puzzle)\u7684\u8b0e\u984c<!--more-->. \u9019\u4e0d\u662f\u624b\u6a5f\u7576\u6a5f\u7684\u554f\u984c, \u9019\u662f\u4e00\u500b\u662f\u6709\u8da3\u7684\u6578\u5b78\u554f\u984c.<\/p>\n<p>\u5df2\u6545\u5df4\u897f\u6578\u5b78\u5bb6\u517c\u4f5c\u5bb6\u99ac\u723e\u5df4\u5854\u7f55(Malba Tahan)\u6709\u672c\u77e5\u540d\u7684\u6578\u5b78\u7ae5\u756b\u66f8<strong>\u300a\u6578\u5b78\u5929\u65b9\u591c\u8b5a\uff1a\u6492\u7c73\u723e\u7684\u5947\u5e7b\u4e4b\u65c5\u300b<\/strong>\u7528\u6709\u8da3\u7684\u65b9\u6cd5\u4ecb\u7d39\u6578\u5b78\u8207\u963f\u62c9\u4f2f\u6587\u5316\u7684\u7f8e. \u9019\u672c\u66f8\u7684\u4f5c\u8005, \u99ac\u723e\u5df4\u5854\u7f55, \u672c\u540d\u662f J\u00falio C\u00e9sar de Mello e Souza (1895-1974)\u662f\u4e00\u4f4d\u5df4\u897f\u7684\u6578\u5b78\u5bb6\u517c\u4f5c\u5bb6\u3010\u8a3b2\u3011.<br \/>\n<center><\/p>\n<div class=\"imgbox\" style=\"width: 640px\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/morrisjfwong.com\/blog\/wp-content\/uploads\/2013\/06\/90-apples-puzzle.png\" alt=\"90-apples-puzzle\" width=\"640\" height=\"320\" class=\"alignnone size-full wp-image-5969\" \/><\/p>\n<p class=\"imginfo\">90 Apples Math Puzzle.<\/p>\n<\/div>\n<p><\/center><\/p>\n<h6>\u4e5d\u5341\u500b\u860b\u679c\u7684\u8b0e\u984c<\/h6>\n<p>\u8b0e\u984c\u6545\u4e8b\u662f\u9019\u6a23\u958b\u59cb\u7684. \u963f\u62c9\u4f2f\u7684\u53e4\u570b\u4e2d, \u4e09\u59ca\u59b9\u63a5\u5230\u5b98\u54e1\u4e00\u500b\u7121\u7406\u7684\u8981\u6c42: \u8ce3\u51fa\u4e5d\u5341\u500b\u860b\u679c, \u4e0d\u904e\u5fc5\u9808\u9075\u5b88\u4e0b\u9762\u689d\u4ef6:<\/p>\n<blockquote>\n<div class=\"bqtitle\">\u860b\u679c\u7684\u8b0e\u984c \u5b98\u54e1\u7684\u8981\u6c42:<\/div>\n<p>(1) \u8001\u5927\u8ce3\u51fa50\u500b\u860b\u679c, \u8001\u4e8c\u8ce3\u51fa30\u500b\u860b\u679c, \u8001\u4e09\u8ce3\u51fa10\u500b\u860b\u679c.<br \/>\n(2) \u50f9\u683c\u7531\u8001\u5927\u6c7a\u5b9a, \u8001\u4e8c\u8001\u4e09\u5fc5\u9808\u63a1\u7528\u76f8\u540c\u65bc\u8001\u5927\u7684\u50f9\u683c.<br \/>\n(3) \u4e09\u59ca\u59b9\u5fc5\u9700\u8981\u5e36\u56de\u76f8\u540c\u7684\u9322 (\u7e3d\u6536\u5165\u4e09\u4eba\u5fc5\u9808\u76f8\u540c).<br \/>\n(4) \u860b\u679c\u7576\u7136\u4e0d\u80fd\u8d08\u9001, \u4e1f\u6389\u6216\u5403\u6389!\n<\/p><\/blockquote>\n<p>\u9019\u5c31\u662f\u4e5d\u5341\u500b\u860b\u679c\u7684\u8b0e\u984c( 90 apples math puzzle ), \u5f9e\u7c21\u55ae\u7684\u6578\u5b78\u76f4\u89ba\u4f86\u770b, \u4f3c\u4e4e\u662f\u4e0d\u53ef\u80fd\u9054\u6210\u7684\u4efb\u52d9, \u6839\u672c\u662f\u5b98\u54e1\u7121\u7406\u7684\u8981\u6c42, \u4e0d\u904e, \u5176\u5be6\u554f\u984c\u4e2d\u537b\u96b1\u85cf\u8457\u8457\u7121\u9650\u53ef\u80fd\u5594!<\/p>\n<h6>\u89e3\u6cd5\u4e00: \u514d\u8cbb\u7684\u860b\u679c<\/h6>\n<p>\u60f3\u6cd5\u4e00, \u5047\u8a2d\u4e00\u9846\u860b\u679c\u7684\u50f9\u683c\u662fP, \u5247\u6211\u5011\u7b2c\u4e00\u7a2e\u60f3\u6cd5\u6703\u8b8a\u6210\u662f:<\/p>\n<p><center><strong>50*P = 30*P = 10*P = \u7e3d\u6536\u5165<\/strong><\/center><\/p>\n<p>\u9019\u53ea\u6709\u4e00\u500b\u89e3\u6cd5, \u5c31\u662f P=0 \u514d\u8cbb\u7684\u860b\u679c, \u4f46\u9019\u4e0d\u7b26\u898f\u5b9a, \u56e0\u6b64\u89e3\u6cd5\u4e0d\u5982\u6b64\u55ae\u7d14.<\/p>\n<h6>\u89e3\u6cd5\u4e8c: \u771f\u6b63\u53ef\u884c\u7684\u860b\u679c\u8ce3\u6cd5<\/h6>\n<p>\u66f8\u4e2d\u7684<strong>\u6578\u6578\u4eba\u6492\u7c73\u723e<\/strong>\u63d0\u51fa\u4e86\u4e00\u500b\u89e3\u6cd5\u4f86\u89e3\u6c7a\u4e5d\u5341\u500b\u860b\u679c\u7684\u8b0e\u984c, \u4e0d\u904e, \u5176\u5be6\u89e3\u6cd5\u6709\u7121\u9650\u591a\u7a2e, \u5176\u4e2d\u5305\u542b\u81f3\u5c1140\u7a2e\u3010\u8a3b1\u3011\u89e3\u7b54\u7d44\u5408. \u672c\u66f8\u7684\u4f5c\u8005\u4e26\u6c92\u6709\u63d0\u51fa\u5b8c\u6574\u7684\u89e3\u6cd5\u7b54\u6848, \u9019\u88e1, \u8b93\u9b54\u65c5\u58eb\u4f86\u7528\u4e00\u500b\u65b0\u7684\u89e3\u6cd5\u5b8c\u6574\u89e3\u51fa\u6240\u6709\u7684\u7b54\u6848.<\/p>\n<p>\u9996\u5148, \u6211\u5011\u505a\u4e00\u4e9b\u5047\u8a2d\u4ee5\u65b9\u4fbf\u8a08\u7b97:<\/p>\n<blockquote><p>\n(A-1) \u5047\u8a2d\u860b\u679c\u5206\u5169\u6279\u8ce3\u51fa. \u7b2c\u4e00\u6279\u860b\u679c\u50f9\u683c\u662fP, \u7b2c\u4e8c\u6279\u50f9\u683c\u662fQ.<br \/>\n(A-2) \u8001\u5927\u7b2c\u4e00\u6279\u8ce3\u51fa X \u500b\u860b\u679c, \u5247\u7b2c\u4e8c\u6279\u8ce3\u51fa 50-X \u500b\u860b\u679c.<br \/>\n(A-3) \u8001\u4e8c\u7b2c\u4e00\u6279\u8ce3\u51fa Y \u500b\u860b\u679c, \u5247\u7b2c\u4e8c\u6279\u8ce3\u51fa 30-Y \u500b\u860b\u679c.<br \/>\n(A-4) \u8001\u4e09\u7b2c\u4e00\u6279\u8ce3\u51fa Z \u500b\u860b\u679c, \u5247\u7b2c\u4e8c\u6279\u8ce3\u51fa 10-Z \u500b\u860b\u679c.<br \/>\n(A-5) \u6700\u5f8c\u6bcf\u500b\u4eba\u90fd\u62ff\u56de A \u5143\u91d1\u9322.\n<\/p><\/blockquote>\n<p>\u6211\u5011\u53ef\u4ee5\u5217\u51fa\u4e0b\u9762\u7684\u95dc\u4fc2\u5f0f:<br \/>\n<center><strong>P*X + Q*(50-X) = A   &#8230;..(B-1\u5f0f) \u8001\u5927\u7684\u7e3d\u6536\u5165<br \/>\nP*Y + Q*(30-Y) = A   &#8230;..(B-2\u5f0f) \u8001\u4e8c\u7684\u7e3d\u6536\u5165<br \/>\nP*Z + Q*(10-Z) = A   &#8230;..(B-2\u5f0f) \u8001\u4e09\u7684\u7e3d\u6536\u5165<br \/>\n<\/strong><\/center><\/p>\n<p>\u5982\u679c\u6211\u5011\u628a (B-1\u5f0f)(B-2\u5f0f)(B-2\u5f0f) \u6539\u5beb, \u53ef\u4ee5\u5f97\u5230:<br \/>\n<center>(P-Q)X = A-50*X   &#8230;..(B-3\u5f0f)<br \/>\n(P-Q)Y = A-30*Y   &#8230;..(B-4\u5f0f)<br \/>\n(P-Q)Z = A-10*Z   &#8230;..(B-5\u5f0f)<br \/>\n<\/center><\/p>\n<p>\u5982\u679c\u6211\u5011\u628a\u50f9\u683c\u8207\u6578\u91cf\u5206\u6210\u5806\u7684\u904b\u7b97\u6982\u5ff5\u5f15\u5165. \u56e0\u6b64\u6211\u5011\u628a (B-4\u5f0f)\u6e1b\u53bb(B-3\u5f0f), \u540c\u7406 (B-5\u5f0f)\u6e1b\u53bb(B-4\u5f0f), \u540c\u7406 (B-5\u5f0f)\u6e1b\u53bb(B-3\u5f0f) \u6211\u5011\u53ef\u4ee5\u5f97\u5230:<br \/>\n<center>(P-Q)*(Y-X) = 20*Q   &#8230;..(C-1\u5f0f)<br \/>\n(P-Q)*(Z-Y) = 20*Q   &#8230;..(C-2\u5f0f)<br \/>\n(P-Q)*(Z-X) = 40*Q   &#8230;..(C-3\u5f0f)<br \/>\n<\/center><\/p>\n<p>\u6211\u5011\u77e5\u9053(C-1\u5f0f)\u8207(C-2\u5f0f)\u76f8\u7b49, \u56e0\u6b64\u5f97\u5230:<br \/>\n<center>(Y-X) = (Z-Y) \u4e5f\u5c31\u662f <strong>Z = 2*Y &#8211; X  &#8230;..(D-1\u5f0f)<\/strong><br \/>\n<\/center><\/p>\n<p>\u9019\u88e1\u6709\u4e00\u500b\u76f4\u5f97\u8a0e\u8ad6\u7684\u5730\u65b9: \u7576 P=Q, \u4e5f\u5c31\u662f\u5169\u6b21\u860b\u679c\u8ca9\u552e\u7684\u50f9\u683c\u76f8\u540c\u6642, \u4e0a\u9762\u7684\u7b49\u5f0f\u4e5f\u6703\u6210\u7acb. \u4e0d\u904e\u9019\u60c5\u6cc1\u660e\u986f\u7121\u6cd5\u9054\u6210\u4efb\u52d9! \u56e0\u6b64\u4e0d\u4e88\u8003\u616e. \u5beb\u5230\u9019\u88e1, \u4e5f\u8a31\u4f60\u5df2\u7d93\u6709\u9ede\u770b\u82b1\u4e86, \u7c21\u55ae\u8aaa\u7d50\u8ad6: \u9019\u544a\u8a34\u6211\u5011\u4e09\u59ca\u59b9\u8ce3\u51fa\u7684\u860b\u679c\u6578\u91cf\u6709\u8457 Z=2*Y-X \u7684\u95dc\u4fc2\u5f0f.<\/p>\n<h6>\u50f9\u683cP\u8207Q<\/h6>\n<p>\u63a5\u4e0b\u4f86\u6211\u4f86\u89e3\u6c7a\u50f9\u683c\u554f\u984c, \u9996\u5148:<br \/>\n<center>\u5047\u8a2d <strong>K = (Y-X)  &#8230;..(D-2\u5f0f)<\/strong><\/center><\/p>\n<p>\u56e0\u6b64, \u6211\u5011\u53ef\u4ee5\u628a (C-1\u5f0f) \u4fee\u6539\u70ba:<br \/>\n<center><br \/>\n(P-Q)*(Y-X) = (P-Q)*K = 20*Q  &#8230;..(E-1\u5f0f)<\/center><br \/>\n<center>P = ((20+K)\/K)*Q   &#8230;..(E-2\u5f0f)<\/center><br \/>\n<center>\u5047\u8a2d: <strong>ratio = ((20+K)\/K)   &#8230;..(E-3\u5f0f)<\/strong><\/center><br \/>\n<center>P = ratio * Q   &#8230;..(E-4\u5f0f) \u524d\u5f8c\u5169\u6b21\u860b\u679c\u552e\u50f9\u7684\u95dc\u4fc2<\/center><\/p>\n<p>\u8cd3\u679c! \u5176\u5be6, \u5230\u9019\u88e1\u6211\u5011\u5df2\u7d93\u628a\u860b\u679c\u7684\u8b0e\u984c\u89e3\u6c7a\u5566! \u95dc\u9375\u7684\u7b54\u6848\u5c31\u5728\u4ee5\u4e0b\u5169\u5f0f\u4e2d:<br \/>\n<center><strong><br \/>\nZ = 2 * Y &#8211; X   &#8230;..(D-1\u5f0f) \u860b\u679c\u6578\u91cf\u95dc\u4fc2<br \/>\nP = ratio * Q   &#8230;..(E-4\u5f0f) \u860b\u679c\u552e\u50f9\u95dc\u4fc2<br \/>\n<\/strong><\/center><\/p>\n<p>\u53ea\u8981\u6211\u5011\u8a08\u7b97\u51fa X, Y, Z\u3000\u7684\u6578\u5b57\u7d44\u5408, \u4e5f\u5c31\u53ef\u4ee5\u5b9a\u7fa9\u51fa P, Q \u7684\u95dc\u4fc2.<\/p>\n<h6>\u5b8c\u6574 40 \u7a2e\u860b\u679c\u89e3\u6cd5 + \u7121\u9650\u53ef\u80fd<\/h6>\n<p>\u63a5\u8457\u6211\u628a\u5b8c\u6574\u7684\u89e3\u7b5440\u7a2e\u3010\u8a3b1\u3011\u8a08\u7b97\u51fa\u4f86. \u4e00\u822c\u4f86\u8aaa, \u8981\u6c42\u51fa\u9019\u7a2e\u591a\u7d44\u5408\u554f\u984c\u7528\u7d19\u7b46\u662f\u5f88\u56f0\u96e3\u7684, \u56e0\u6b64\u6211\u5011\u642c\u51fa\u96fb\u8166\u7684\u8a66\u7b97\u8868! \u4f60\u53ef\u4ee5\u7528 Excel \u6216\u662f OpenOffice Cal \u6216\u662f\u4efb\u4e00\u7a2e\u8a66\u7b97\u8868\u4f86\u4f5c\u8a08\u7b97.<\/p>\n<p>\u9996\u5148, \u6211\u5011\u77e5\u9053X, Y,Z \u7684\u95dc\u9375\u91cd\u9ede\u5728\u65bc\u9019\u4e9b\u6578\u5b57\u90fd\u662f\u6b63\u6574\u6578.<br \/>\n<center><br \/>\n<strong>0 <= X <= 50 \u4e14 X = \u6574\u6578(integer)<\/strong><br \/>\n<strong>0 <= Y <= 30 \u4e14 Y = \u6574\u6578(integer)<\/strong><br \/>\n<strong>0 <= Z <= 10 \u4e14 Z = \u6574\u6578(integer)<\/strong><br \/>\n<\/center><\/p>\n<p>\u8868\u683c\u4e00, \u4f9d\u64da X, Y, Z \u7684\u9650\u5236\u7bc4\u570d, \u53ef\u4ee5\u4f9d\u64da (D-1\u5f0f) \u6c42\u51fa\u6240\u6709\u7684\u6578\u5b57\u7d44\u5408. \u56e0\u6b64, \u6211\u5011\u53ef\u4ee5\u4f9d\u64da\u4e09\u59ca\u59b9\u7684\u860b\u679c\u6578\u76ee\u5f97\u5230\u4ee5\u4e0b\u95dc\u4fc2: \u7070\u82720-10\u4ee3\u8868Z, \u7070\u82720-30\u4ee3\u8868Y, \u800c\u7d05\u5b57\u4ee3\u8868\u8a08\u7b97\u51fa\u7684 Z \u503c.<br \/>\n<center><\/p>\n<div class=\"imgbox\" style=\"width: 637px\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/morrisjfwong.com\/blog\/wp-content\/uploads\/2013\/06\/90apples-XYZ-001a.png\" alt=\"90apples-XYZ-001a\" width=\"637\" height=\"353\" class=\"alignnone size-full wp-image-5958\" \/><\/p>\n<p class=\"imginfo\">\u8868\u683c\u4e00, \u6240\u6709\u7684 X, Y, Z \u7684\u6578\u5b57\u7d44\u5408.<\/p>\n<\/div>\n<p><\/center><\/p>\n<p>\u8868\u683c\u4e8c, \u4f9d\u64da\u8868\u683c\u4e00\u6240\u6709\u7684 X, Y, Z \u7684\u6578\u5b57\u7d44\u5408\u53ef\u4ee5\u6839\u64da (E-3\u5f0f) \u8a08\u7b97\u51fa ratio \u503c. \u5176\u4e2d\u5fc5\u9808\u8a2d\u5b9a\u5e7e\u500b\u9650\u5236\u689d\u4ef6\u4f86\u7be9\u9078 Ratio \u7684\u6578\u503c, \u9019\u4e9b\u689d\u4ef6\u662f:<br \/>\n<center><br \/>\n<strong>ratio >= 0   &#8230;..(E-5\u5f0f) \u50f9\u683c\u5fc5\u9808\u662f\u6b63\u6578, \u56e0\u6b64 ratio \u70ba\u6b63\u503c.<\/strong><br \/>\n<\/center><br \/>\n<center><br \/>\n<strong>0 <= Z <= 10 \u4e14 Z = \u6574\u6578(integer)<\/strong><br \/>\n<\/center><\/p>\n<p>\u5f9e\u9019\u88e1\u6211\u5011\u53ef\u4ee5\u770b\u5230\u6240\u6709\u7684 40 \u7d44\u89e3\u7b54\u7d44\u6210. \u5176\u4e2d\u50f9\u683c\u7684\u6bd4\u7387\u7e3d\u5171\u6709\u4e5d\u7a2e <strong>( ratio = 1\/5, 1\/6, 3\/23, 1\/11, 1\/21, 6, 23\/3, 11, 21 \u6b63\u597d\u90fd\u662f\u76f8\u4e92\u7684\u5012\u6578 )<\/strong>. \u9019\u89e3\u6cd5\u4e2d\u537b\u6709\u8457\u4e00\u500b\u5c0f\u7955\u5bc6: \u5982\u679c\u6211\u5011\u7b49\u6bd4\u7387\u5c07 P,Q \u653e\u5927\u7e2e\u5c0f, \u5247\u53ef\u4ee5\u5f97\u5230\u7121\u9650\u591a\u7a2e\u7684\u89e3\u7b54!!<br \/>\n<center><\/p>\n<div class=\"imgbox\" style=\"width: 637px\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/morrisjfwong.com\/blog\/wp-content\/uploads\/2013\/06\/90apples-ratio-001a.png\" alt=\"90apples-ratio-001a\" width=\"637\" height=\"353\" class=\"alignnone size-full wp-image-5959\" \/><\/p>\n<p class=\"imginfo\">\u8868\u683c\u4e8c, \u4f9d\u64da X, Y, Z \u6578\u8a08\u7b97\u51fa ratio \u503c, \u53ef\u4ee5\u89e3\u51fa\u860b\u679c\u552e\u50f9\u95dc\u4fc2.<\/p>\n<\/div>\n<p><\/center><\/p>\n<p>\u8868\u683c\u4e09, \u4f9d\u64da\u6240\u6709\u7684 X, Y, Z, P\/Q ratio \u7684\u7d44\u5408\u53ef\u4ee5\u6c42\u51fa\u4e09\u59ca\u59b9\u8ce3\u860b\u679c\u5f97\u5230\u7684\u91d1\u9322.<\/p>\n<p><center><\/p>\n<div class=\"imgbox\" style=\"width: 637px\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/morrisjfwong.com\/blog\/wp-content\/uploads\/2013\/06\/90apples-A-001a.png\" alt=\"90apples-A-001a\" width=\"637\" height=\"353\" class=\"alignnone size-full wp-image-5960\" \/><\/p>\n<p class=\"imginfo\">\u8868\u683c\u4e09, \u4e09\u59ca\u59b9\u8ce3\u860b\u679c\u5f97\u5230\u7684\u91d1\u9322.<\/p>\n<\/div>\n<p><\/center><\/p>\n<h6>90\u500b\u860b\u679c\u7684\u8b0e\u984c &#8211; \u89e3\u7b54\u8207\u7d50\u8ad6<\/h6>\n<p>\u4f9d\u64da\u9019\u6574\u500b\u6578\u5b78\u7684\u8a08\u7b97\u5206\u6790\u904e\u7a0b, \u6211\u5011\u53ef\u4ee5\u5f97\u77e5\u5e7e\u500b\u7d50\u8ad6 : (1) \u9019\u4e26\u4e0d\u662f\u4e00\u500b\u53ea\u6709\u552f\u4e00\u7a2e\u89e3\u7b54\u7684\u8b0e\u984c, \u4e8b\u5be6\u4e0a, \u9019\u500b90\u500b\u860b\u679c\u8b0e\u984c\u6709\u845740\u7a2e\u3010\u8a3b1\u3011\u89e3\u6cd5\u7d44\u5408. (2) \u50f9\u683c\u7684\u7d44\u5408\u6703\u6709\u4e5d\u7a2e, \u5176\u4e2d\u5169\u5169\u4e92\u70ba\u5012\u6578 (3) \u5982\u679c\u628a\u50f9\u683c\u4f9d\u64da\u500d\u6578\u653e\u5927\u7e2e\u5c0f, \u5247\u53ef\u4ee5\u5f97\u5230\u7121\u9650\u591a\u7a2e\u7684\u89e3\u7b54!<\/p>\n<p>\u4e5f\u8a31\u300a\u6578\u5b78\u5929\u65b9\u591c\u8b5a\uff1a\u6492\u7c73\u723e\u7684\u5947\u5e7b\u4e4b\u65c5\u300b\u4e2d\u7684<strong>\u6578\u6578\u4eba\u6492\u7c73\u723e<\/strong>\u4e26\u6c92\u6709\u60f3\u5230, \u539f\u4f86\u6578\u5b78\u63d0\u4f9b\u4e86\u7121\u9650\u7684\u53ef\u80fd, \u5049\u5927\u7684\u963f\u62c9!<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/morrisjfwong.com\/blog\/images\/morrisjfwong-favicon-bw.png\" class=\"end\" alt=\"\" title=\"\" width=\"14\" height=\"14\" \/><\/p>\n<h6>\u53c3\u8003\u8cc7\u6599<\/h6>\n<p>\u3010\u8a3b\u3011: \u56b4\u683c\u8aaa\u8d77\u4f86, \u61c9\u8a72\u6709\u845745\u7a2e\u7684\u89e3\u6cd5\u7d44\u5408. \u4e0d\u904e, \u5982\u679c\u7576\u6700\u5e74\u8f15\u7684\u8001\u4e09\u7b2c\u4e00\u6b21\u8ce3\u51fa 0 \u500b\u860b\u679c\u7684\u60c5\u6cc1\u88ab\u8996\u70ba\u4e0d\u5408\u898f\u5247\u6642, \u53ea\u6703\u5269\u4e0b40\u7a2e\u7684\u89e3\u6cd5\u7d44\u5408.<br \/>\n\u3010\u8a3b\u3011: <a href=\"http:\/\/www.cite.com.tw\/product_info.php?products_id=29991\" target=\"_blank\">\u300a\u6578\u5b78\u5929\u65b9\u591c\u8b5a\uff1a\u6492\u7c73\u723e\u7684\u5947\u5e7b\u4e4b\u65c5\u300b<\/a>, \u4f5c\u5bb6\u99ac\u723e\u5df4\u5854\u7f55(<a href=\"http:\/\/en.wikipedia.org\/wiki\/Malba_Tahan\" target=\"_blank\">Malba Tahan<\/a>) \u672c\u540d\u662f J\u00falio C\u00e9sar de Mello e Souza (1895-1974)\u662f\u4e00\u4f4d\u5df4\u897f\u7684\u6578\u5b78\u5bb6\u517c\u4f5c\u5bb6. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u860b [&#038;hellip<\/p>\n","protected":false},"author":1,"featured_media":5969,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[247,269],"class_list":["post-5946","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math","tag-247","tag-269"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u860b\u679c\u7684\u8b0e\u984c<\/title>\n<meta name=\"description\" content=\"\u860b\u679c\u7684\u8b0e\u984c: \u6211\u5011\u8981\u4f86\u89e3\u6c7a\u4e00\u500b90\u500b\u860b\u679c(90 apples puzzle)\u7684\u8b0e\u984c. \u9019\u4e0d\u662f\u624b\u6a5f\u7576\u6a5f\u7684\u554f\u984c, \u9019\u662f\u4e00\u500b\u662f\u6709\u8da3\u7684\u6578\u5b78\u554f\u984c. \u5df2\u6545\u5df4\u897f\u6578\u5b78\u5bb6\u517c\u4f5c\u5bb6\u99ac\u723e\u5df4\u5854\u7f55(Malba Tahan)\u6709\u672c\u77e5\u540d\u7684\u6578\u5b78\u7ae5\u756b\u66f8\u300a\u6578\u5b78\u5929\u65b9\u591c\u8b5a\uff1a\u6492\u7c73\u723e\u7684\u5947\u5e7b\u4e4b\u65c5\u300b\u7528\u6709\u8da3\u7684\u65b9\u6cd5\u4ecb\u7d39\u6578\u5b78\u8207\u963f\u62c9\u4f2f\u6587\u5316\u7684\u7f8e.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/morrisjfwong.com\/blog\/90-apples-puzzle-math-solution\/\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005:\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u9b54\u65c5\u58eb\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9810\u4f30\u95b1\u8b80\u6642\u9593\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 \u5206\u9418\" \/>\n<script type=\"application\/ld+json\" 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\u6211\u5011\u8981\u4f86\u89e3\u6c7a\u4e00\u500b90\u500b\u860b\u679c(90 apples puzzle)\u7684\u8b0e\u984c. \u9019\u4e0d\u662f\u624b\u6a5f\u7576\u6a5f\u7684\u554f\u984c, \u9019\u662f\u4e00\u500b\u662f\u6709\u8da3\u7684\u6578\u5b78\u554f\u984c. \u5df2\u6545\u5df4\u897f\u6578\u5b78\u5bb6\u517c\u4f5c\u5bb6\u99ac\u723e\u5df4\u5854\u7f55(Malba Tahan)\u6709\u672c\u77e5\u540d\u7684\u6578\u5b78\u7ae5\u756b\u66f8\u300a\u6578\u5b78\u5929\u65b9\u591c\u8b5a\uff1a\u6492\u7c73\u723e\u7684\u5947\u5e7b\u4e4b\u65c5\u300b\u7528\u6709\u8da3\u7684\u65b9\u6cd5\u4ecb\u7d39\u6578\u5b78\u8207\u963f\u62c9\u4f2f\u6587\u5316\u7684\u7f8e.\",\"breadcrumb\":{\"@id\":\"https:\/\/morrisjfwong.com\/blog\/90-apples-puzzle-math-solution\/#breadcrumb\"},\"inLanguage\":\"zh-TW\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/morrisjfwong.com\/blog\/90-apples-puzzle-math-solution\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-TW\",\"@id\":\"https:\/\/morrisjfwong.com\/blog\/90-apples-puzzle-math-solution\/#primaryimage\",\"url\":\"https:\/\/morrisjfwong.com\/blog\/wp-content\/uploads\/2013\/06\/90-apples-puzzle.png\",\"contentUrl\":\"https:\/\/morrisjfwong.com\/blog\/wp-content\/uploads\/2013\/06\/90-apples-puzzle.png\",\"width\":640,\"height\":320},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/morrisjfwong.com\/blog\/90-apples-puzzle-math-solution\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"BLOG\",\"item\":\"https:\/\/morrisjfwong.com\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u860b\u679c\u7684\u8b0e\u984c\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/morrisjfwong.com\/blog\/#website\",\"url\":\"https:\/\/morrisjfwong.com\/blog\/\",\"name\":\"\u9b54\u65c5\u58eb 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